One of the most important measurements in biomedical research is the determination of blood flow and tissue perfusion. Although a few noninvasive methods have been studied extensively, these are limited in application and accuracy. With the development of sophisticated solid-state devices for heating and sensing temperature, it is now possible to optimally design a measurement system and experimental protocol to estimate flow in a given tissue. Sensors can be fabricated in arrays of small individual elements that can each produce a specified time-varying temperature. For such a sensor to be optimally designed to evaluate perfusion, it is necessary to develop a mathematical model of heat transfer that incorporates sufficient detail of the structure and properties of the tissue being measured and of the device itself. The underlying hypothesis is that by producing a temperature change at the tissue surface the subsequent dynamics of the heat transfer rate measured at the same surface will depend on the blood flow of the underlying tissue. Consequently, it should be possible to interpret the sensor response to perfusion at different depths and, thus, to estimate the blood flow in different layers. To establish specifications of a multi-element, multi-temperature heat flux sensor for estimating perfusion, we shall use a mathematical model to simulate the dynamic responses of the system. Furthermore, we can determine conditions under which the responses are most sensitive and specific to blood flow. With this information, we can develop simplified models to obtain a practical method of signal processing. The initial goal is to evaluate the dermal capillary-loop perfusion. The measurement of skin perfusion and blood flow is important in understanding normal skin physiology, thermal regulation, skin pathology and conditions relating continuously monitored transcutaneous oxygen tension (a widely applied instrument in critical care medicine) with central arterial values. Although skin perfusion is important in its own right, it is also essential for evaluating transcutaneous oxygen tension by surface electrodes. Furthermore, if this basic approach is feasible, then it can be applied to other medical applications for the noninvasive evaluation of blood flow deeper in tissues.